If you're just going for target practice and for fun it doesn't really matter. Just use whatever makes you happy. I've had both modern compound bows and old school longbows. The compound bows are much better for accuracy and distance, but there is less **** that can go wrong with a longbow or a recurve since they're so much simpler. But some of the newer recurves are pretty high tech in and of themselves. They use glass laminate materials, string silencers, and all other manner of bells and whistles that someone thinks you may be willing to buy. Also, I always preferred the finger tab or the archery glove to protect my fingers. I had a trigger activated release for my compound bow, but it felt uncomfortable having these little locking jaws being all that was holding the string. However, it did make for much cleaner and quicker string releases.

I'm thinking of buying my own bow in the coming weeks, so I want to have an idea of what I'm looking for beforehand.

I'm looking for target-shooting gear, rather than hunting or flight. I have a preference for recurve bows, because I'm not a woman. I don't need pullies to do my work!

So far I've been renting a bow during class, all of which are twenty-five pounders. Strength-wise I could probably handle a much heavier bow, but I don't want to buy a five-billion pound death bow only to find out that I can't keep good form. What's a good poundage to move up to? Should I get wood or synthetics? I'm going to get a sight, of course, but should I bother with any of the fancy accessories? Would stabliziers really matter at this point?

What should I look for in arrows, aside from the proper length?

I've been using a leather tab during class. Should I just stick with tabs? Are there any advantages to the gloves? Are bracers bracers, or should I look for something in particular? And what of the different types of quivers?

Couple of things to think about...
1. Even if you are only interested in target shooting, you can still consider getting a hunting bow. The National Field Archery Association sponsors several outdoor shoots, and my own personal opinion is that walking a range and shooting at targets or animal dummies is incredibly fun. Plus, field archers are fantastically fun and friendly, and you will learn a lot from them.
2. I have a preference for long bows - ever since I saw Howard Hill stunt shoot for Errol Flynn in the old Robin Hood movies. Plus, I've noted that a lot of trick shooters prefer the long bow to the recurve...more stable, and less finicky. The other thing is that there is a certain romance to bare bow shooting with a long bow ( some might argue about whether today's long bows are really more like the Native American flatbows, but that is a beyond this post).
3. Regarding poundage, it depends on your style of shooting, and what your goals are. Olympic archers will hold the bow perpendicular to the ground, and line up the target with sights - hence the need for lighter pound bows so that the draw can be held longer. Barebow shooters do it instinctively - that is, once they touch the hand to the anchor point, they let go, aiming much in the way that you and I would throw a ball. As such, barebow guys can go much heavier on the poundage. Generally speaking, 45 - 55# is an excellent hunting poundage, but also reasonable for target shooting. If you want to stick with Olympic style, you are probably better off with 35 - 40#. I personally like to use heavier bows, in the 65 to 70# range, but I have a shorter draw length, so I'm not actually pulling that much.
4. If you are sold on a recurve, then today's bows are all wood laminated with fiberglass (I think), though there are custom bowyers who will make wood only recurves (usually for barebow shooters). Reliable big name guys who do recurves are Bear Archery, and Martin Archery. Hoyt is well known in the Olympic archery side, but I don't like the way their bows look...I much prefer the wood handles to the aluminum handles that Hoyt uses.
5. Before you plunk a lot of $$ on a bow, make sure you check out Ebay!!!!! The archery community on Ebay consists of many genuine, avid archers, and you will often find incredible deals there. I myself bought a take down long bow (rare find) and a Howard Hill longbow, both for about 60% of the expected price I would have paid. For other information sites, check out www.stickbow.com, or go to your local magazine rack, and look at Traditional Archery magazine. Another excellent book is the Traditional Bowyers Bible - a great read if you want to appreciate the beauty of the physics of any traditional bow.
6. Regarding stabilizers - some bows have heavy enough handles that you probably don't need a stabilizer. Barebow shooters hate to use accessories - to us, the fun is in hitting a target with just a stick and an arrow :eusa_whis I might encourage you to try shooting without a sight - it's true that you won't be as accurate, but trust me, it is often much more satisfying.
7. Your arrow needs again depend on the style of shooting, and your goals. Competitive target shooters want reliability, and often a flat trajectory when they shoot. It's one of the reasons that aluminum arrows are so popular even with recurves. Also, aluminum arrows don't break as often, or develop kinks and bends, or warp when they hit a patch of wet grass repeatedly. Carbon arrows look too much like toothpicks to me...I've only seen compound shooters use them, and my personal opinion is that they just aren't that satisfying to use. My personal preferences are to wood arrows - finicky, heavy, but just beautiful to see a wood arrow go in flight.
8. No real difference between finger tabs and gloves. I like tabs better just because my fingers breathe more. As for braces, any standard brace will do. Experienced bare bow shooters will usually never hit their arm anyway, because the bow is held at a slight cant, and the bow arm is slightly bent on the draw. As for quivers, most target shooters prefer hip quivers...holds a lot of arrows, and easy to access. I love the back quiver (it's got to be leather :-) ), and then there are the hunters who prefer bow quivers, so you don't have to reach to far for your arrow without spooking the prey.

I would recommend you check to see if there any traditional archery clubs in the area, and just meet up with and talk to folks...as I said, they are incredibly friendly, and love to share their art. Good luck on your endeavours! I fell in love with archery almost twenty years ago...started out with a compound, then switched to recurve, then long bow, and haven't looked back since. I wish I could shoot more than I do (most of my free time is spent with wife, daughter, and bjj right now) and anyway, in my suburbs my neighbors would freak if they saw me walking around in full hunting gear (I don't hunt, by the way, I just love using hunting bows).

I strongly suggest that you buy your first bow from a real pro shop. The help that you're going to get from an experienced salesperson who truely loves the sport is worth paying extra. The last thing you need is some no-nothing at a sporting goods store (no offense emevas) talking from his extremely limited experience and being led by the blind. Getting your equipment on the internet: not the best option either. You're going to have to have your draw measured anyway (unless you know it already) and your arrows cut/sized w/e, so you might as well go into a pro shop and do a one-stop-shop; tell them everything you've mentioned here and more. Getting a quality used bow from pro shops can be good too, often experienced folks working their way up through bow will trade theirs in with barely a scratch and you'll be able to own a bow that would otherwise be way out of your price range.

My personal preference is for recurve, I have a 66" Sky Medalist at the moment and I shoot aluminum arrows, which I love/hate and I prefer a tab, although it can be annoying at times. It's 45# which it still light enough to keep a steady arm, I would suggest in the 35-50# range depending on your size, but it's not all that amazingly important, 25# is maybe bit light though.

The instructor is pressuring me into getting a big sexy competition bow and recommended the Hoyt Matrix or Aerotech risers. They're both pretty sexy, but is the difference in price between the Aerotech and Matrix worthwhile? Is the Aerotech really that much sexier?